Let's see what to do buddy....
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Remember from now on ,
rang = output
and also Remember ,
output = y = f(x)
So : range = f(x)
So we must put the range number instead of f(x) and solve for x.
Let's do it...
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[tex]f(x) = 1[/tex]
[tex] - 4x + 9 = 1[/tex]
Both sides minus 9
[tex] - 4x = 1 - 9[/tex]
[tex] - 4x = - 8[/tex]
Negatives simplified
[tex]4x = 8[/tex]
Divided both sides by 4
[tex]x = \frac{8}{4} \\ [/tex]
[tex]x = 2[/tex]
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[tex]f(x) = - 3[/tex]
[tex] - 4x + 9 = - 3[/tex]
[tex] - 4x = - 3 - 9[/tex]
[tex] - 4x = - 12[/tex]
[tex]4x = 12[/tex]
[tex]x = \frac{12}{4} \\ [/tex]
[tex]x = 3[/tex]
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[tex]f(x) = - 7[/tex]
[tex] - 4x + 9 = - 7[/tex]
[tex] - 4x = - 7 - 9[/tex]
[tex] - 4x = - 16[/tex]
[tex]4x = 16[/tex]
[tex]x = \frac{16}{4} \\ [/tex]
[tex]x = 4[/tex]
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[tex]f(x) = - 15[/tex]
[tex] - 4x + 9 = - 15[/tex]
[tex] - 4x = - 15 - 9[/tex]
[tex] - 4x = - 24[/tex]
[tex]4x = 24[/tex]
[tex]x = \frac{24}{4} \\ [/tex]
[tex]x = 6[/tex]
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[tex]f(x) = - 19[/tex]
[tex] - 4x + 9 = - 19[/tex]
[tex] - 4x = - 19 - 9[/tex]
[tex] - 4x = - 28[/tex]
[tex]4x = 28[/tex]
[tex]x = \frac{28}{4} \\ [/tex]
[tex]x = 7[/tex]
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[tex]f(x) = - 23[/tex]
[tex] - 4x + 9 = - 23[/tex]
[tex] - 4x = - 23 - 9[/tex]
[tex] - 4x = - 32[/tex]
[tex]4x = 32[/tex]
[tex]x = \frac{32}{4} \\ [/tex]
[tex]x = 8[/tex]
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So the domain values are :
x = { 2 , 3 , 4 , 6 , 7 , 8 }
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And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
